The equation of SHM of a particle is given as | vedclass

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(B) The given equation of $SHM$ is $2 \frac{d^2x}{dt^2} + 32x = 0$.Dividing by $2$,we get $\frac{d^2x}{dt^2} + 16x = 0$,or $\frac{d^2x}{dt^2} = -16x$

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$\frac{\pi}{2}$

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(B) The given equation of $SHM$ is $2 \frac{d^2x}{dt^2} + 32x = 0$.Dividing by $2$,we get $\frac{d^2x}{dt^2} + 16x = 0$,or $\frac{d^2x}{dt^2} = -16x$ $...(i)$.The standard differential equation of $SHM$ is $\frac{d^2x}{dt^2} = -\omega^2x$ $...(ii)$.Comparing equations $(i)$ and $(ii)$,we get $\omega^2 = 16$,which implies $\omega = 4 	ext{ rad/s}$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.Substituting the value of $\omega$,$T = \frac{2\pi}{4} = \frac{\pi}{2} 	ext{ s}$.

The equation of $SHM$ of a particle is given as $2 \frac{d^2x}{dt^2} + 32x = 0$,where $x$ is the displacement from the mean position of rest. The period of its oscillation (in seconds) is

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